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A048152 Triangular array T read by rows: T(n,k) = k^2 mod n, for 1 <= k <= n, n >= 1.

%I A048152 #46 Feb 16 2025 08:32:39
%S A048152 0,1,0,1,1,0,1,0,1,0,1,4,4,1,0,1,4,3,4,1,0,1,4,2,2,4,1,0,1,4,1,0,1,4,
%T A048152 1,0,1,4,0,7,7,0,4,1,0,1,4,9,6,5,6,9,4,1,0,1,4,9,5,3,3,5,9,4,1,0,1,4,
%U A048152 9,4,1,0,1,4,9,4,1,0,1,4,9,3,12,10,10,12,3,9,4,1,0
%N A048152 Triangular array T read by rows: T(n,k) = k^2 mod n, for 1 <= k <= n, n >= 1.
%H A048152 T. D. Noe, <a href="/A048152/b048152.txt">Rows n = 1..100 of triangle, flattened</a>
%H A048152 Eric Weisstein's World of Mathematics, <a href="https://mathworld.wolfram.com/QuadraticResidue.html">Quadratic Residue</a>
%F A048152 T(n,k) = A133819(n,k) mod n, k = 1..n. - _Reinhard Zumkeller_, Apr 29 2013
%F A048152 T(n,k) = (T(n,k-1) + (2k+1)) mod n. - _Andrés Ventas_, Apr 06 2021
%e A048152 Rows:
%e A048152   0;
%e A048152   1, 0;
%e A048152   1, 1, 0;
%e A048152   1, 0, 1, 0;
%e A048152   1, 4, 4, 1, 0;
%e A048152   1, 4, 3, 4, 1, 0;
%t A048152 Flatten[Table[PowerMod[k,2,n],{n,15},{k,n}]] (* _Harvey P. Dale_, Jun 20 2011 *)
%o A048152 (Haskell)
%o A048152 a048152 n k = a048152_tabl !! (n-1) !! (k-1)
%o A048152 a048152_row n = a048152_tabl !! (n-1)
%o A048152 a048152_tabl = zipWith (map . flip mod) [1..] a133819_tabl
%o A048152 -- _Reinhard Zumkeller_, Apr 29 2013
%Y A048152 Cf. A060036.
%Y A048152 Cf. A225126 (central terms).
%Y A048152 Cf. A070430 (row 5), A070431 (row 6), A053879 (row 7), A070432 (row 8), A008959 (row 10), A070435 (row 12), A070438 (row 15), A070422 (row 20).
%Y A048152 Cf. A046071 (in ascending order, without zeros and duplicates).
%Y A048152 Cf. A063987 (for primes, in ascending order, without zeros and duplicates).
%K A048152 nonn,tabl,nice,easy
%O A048152 1,12
%A A048152 _Clark Kimberling_